summation??

2007-05-29 7:17 pm
(a),Expand and simplify (n, summation,r=1) [T(r+1)-T(r)].

(b),Using the result of (a),find the value of (24,summation,r=1) [(√r+1)-√r].


answers:(a).T(n+1)-T(1) , (b).4

How can take that??

回答 (1)

2007-05-29 7:34 pm
✔ 最佳答案
first of all, T(r) is a function of r, and can take any form.

(a)
= T(n+1)-T(n)
+T(n)-T(n-1)
+T(n-1)-T(n-2)
+...
+T(3)-T(2)
+T(2)-T(1)
----------------------
terms cancel each other, so the answer is T(n+1)-T(1)

(b)
simple substitution:
put n=24
T(25)-T(1)
=sqrt(25)-sqrt(1)
=5-1
=4


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